A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study weak super Ricci flow through neckpinch in metric measure spaces.
New method for handling multi-dimensional singular controls with jump costs in mean-field problems.
Study optimal investment and consumption strategies with various transaction costs.
Study absolute continuity of Wasserstein barycenters on manifolds with singular cost functions.
Model cash management under ambiguity using maxmin preferences and diffusion.
Optimal trading strategies for pairs trading have been studied by models that try to find either optimal shares of stocks by assuming no transaction costs or optimal timing of trading fixed numbers of shares of stocks with transaction costs. To find optimal strategies which determine optimally both trade times and numb…
The paper explores the geometric structure of cost functions in multiple dimensions.
We study a parabolic equation for finding solutions to the optimal transport problem on compact Riemannian manifolds with general cost functions. We show that if the cost satisfies the strong MTW condition and the stay-away singularity property, then the solution to the parabolic flow with any appropriate initial condi…
New framework for analyzing games with multi-dimensional singular controls and non-linear jumps.
This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex optimization formulation with a cost function consisting of the sum of a likeliho…
This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions, and we consider a general…
We study a single risky financial asset model subject to price impact and transaction cost over an infinite horizon. An investor needs to execute a long position in the asset affecting the price of the asset and possibly incurring in fixed transaction cost. The objective is to maximize the discounted revenue obtained b…
Study proves optimal controls for stochastic Volterra equations with singular kernels.
We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman eq…
Study optimal control of diffusion processes with infimum or supremum costs.
Paper tackles singularity detection in PDEs using data-driven self-supervised learning.
We consider the stochastic control problem of a financial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark pool. Our framework is flexible enough to allow for price-dependent impact func…
We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in the one-dimensional case. …
Investigates optimal strategies for behavioral control problems with finite variation controls.
We apply stochastic Perron's method to a singular control problem where an individual targets at a given consumption rate, invests in a risky financial market in which trading is subject to proportional transaction costs, and seeks to minimize her probability of lifetime ruin. Without relying on the dynamic programming…
We study the regularity properties of the value function associated with an affine optimal control problem with quadratic cost plus a potential, for a fixed final time and initial point. Without assuming any condition on singular minimizers, we prove that the value function is continuous on an open and dense subset of …
Recently, a novel family of biologically plausible online algorithms for reducing the dimensionality of streaming data has been derived from the similarity matching principle. In these algorithms, the number of output dimensions can be determined adaptively by thresholding the singular values of the input data matrix. …
New methods improve Fisher Matrix approximations for neural networks at low cost.
AI stocks hedge against AI singularity's economic impact.
This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems with singular terminal state constraint and possibly unbounded cost coefficients. The existence result is based on a novel comparison principle for…
Study on inventory management under uncertainty using smooth ambiguity preference.
Consider the problem of a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each intervention on the exchange market leads to a proportional cost whose instantaneous marginal value depends on the current …
This paper concerns the numerical solution of a fully nonlinear parabolic double obstacle problem arising from a finite portfolio selection with proportional transaction costs. We consider the optimal allocation of wealth among multiple stocks and a bank account in order to maximize the finite horizon discounted utilit…
This study examines the topology of singularities in optimal semicouplings between unequal spaces.
Study on hyperbolic elastic flow, proving convergence and quantifying singularities.
This paper studies a finite-fuel two-dimensional degenerate singular stochastic control problem under regime switching that is motivated by the optimal irreversible extraction problem of an exhaustible commodity. A company extracts a natural resource from a reserve with finite capacity, and sells it in the market at a …
Study describes singularities of height functions on specific singular surfaces.
Building upon recent advances in entropy-regularized optimal transport, and upon Fenchel duality between measures and continuous functions , we propose a generalization of the logistic loss that incorporates a metric or cost between classes. Unlike previous attempts to use optimal transport distances for learning, our …
We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we reformulate and reduce the Hamilton-Jacobi-Bellma…
Quantum SVT reduces credit risk analysis costs.
Study portfolio optimization with transaction costs and recursive preferences.
Study describes singularities of distance squared functions on singular surfaces.
The paper classifies singularities of plane congruences and affine distance functions.
Defines Perelman's functionals on manifolds with non-isolated conical singularities.
We study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semi-linear PDE with superlinear gradient, monotone generator and singular terminal value. We also…
We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary conditions for optimality in the form of a mixed relaxed-singular maximum principle in a…
Study empty polar varieties' impact on singular function-germs.
Sharp uncertainty principle for nodal sets in singular spaces.
From linear classifiers to neural networks, image classification has been a widely explored topic in mathematics, and many algorithms have proven to be effective classifiers. However, the most accurate classifiers typically have significantly high storage costs, or require complicated procedures that may be computation…
New invariant distinguishes singular knots and links.
Study oscillatory integrals with degenerate singular points in multivariable phase functions.
Study of light function singularities on surfaces.
Study on weighted cscK metrics on Kähler varieties with singularities.